We show that the low-temperature specific heat $\left(C_p\right)$ of the incommensurate chain-ladder system ${\left\{{\mathrm{CuO}}_2\right\}}_{\alpha }\left\{{\mathrm{Sr}}_2{\mathrm{Cu}}_2{\mathrm{O}}_3\right\}={\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ (for $\alpha =10/7)$ shows a rather large excess contribution of nonmagnetic origin. Diluted Al doping at the Cu site or annealing the crystal in an ${\mathrm{O}}_2$ atmosphere suppresses this feature considerably. Using THz time-domain spectroscopy, we relate the occurrence of excess specific heat to the presence of very low-energy $\left(\sim 1\mathrm{meV}\right)$ gapped phonon modes that originate from the sliding motion of oppositely charged $\left\{{\mathrm{CuO}}_2\right\}$ chain and $\left\{{\mathrm{Sr}}_2{\mathrm{Cu}}_2{\mathrm{O}}_3\right\}$ ladder sheets past each other.

• Received 15 August 2018

DOI:https://doi.org/10.1103/PhysRevB.99.054305